The graph of y = 2(x - 4)^2 is a upward-opening parabola. Points (0, 32), (2, 8), (4, 0), (6, 8), and (8, 32) were plotted to illustrate the shape of the quadratic function.
To graph the function y = 2(x - 4)^2, we can identify points on the graph by selecting values for x and computing the corresponding y values. Below, five points are chosen to illustrate the shape of the quadratic function:
When x = 0: y = 2(0 - 4)^2 = 32
Point: (0, 32)
When x = 2: y = 2(2 - 4)^2 = 8
Point: (2, 8)
When x = 4: y = 2(4 - 4)^2 = 0
Point: (4, 0)
When x = 6: y = 2(6 - 4)^2 = 8
Point: (6, 8)
When x = 8: y = 2(8 - 4)^2 = 32
Point: (8, 32)
Now, plot these points on a coordinate plane and connect them smoothly to represent the graph of y = 2(x - 4)^2. The function is a parabola that opens upwards since the coefficient of the x^2 term is positive.